y=c (c is a constant)
y'=0
y=x^n(n is a positive integer 0
y'=nx^(n-1)
y=sin x; y=csc x ;Y=cos x; y=ces x; y=tan x; y=cot x
y'=cos x; y'=-cot x csc x; y'=-sin x; y'=tan x ces x; y'=1/((cos x)^2); y'=-1/((sin x)^2)
y=a^x; y=e^x
y'=a^ x ln a; y'=e^x
y=log a^x; y=ln x
y'=1/(x ln a); y'=1/x
function sum The derivation rule of, difference, product and quotient
If u=u(x), v=v(x) is differentiable at point x, then u+v or uv, Cu (C is a constant), uv, u/v(v≠) is also derivable at point x. And the following formula holds:
function derivation rule
inverse function derivation rule
Set y=f(x) at (A, b) is monotonous and derivable, and f'(x)≠0, then its inverse function x=ω(y) is also monotonous and derivable in the corresponding interval (c, d), and:
ω'(y)=1/(f'(x))
Derivative of inverse trigonometric function
Inverse trigonometric function derivation rule
Compound function derivation rule
If u=ω(x) is derivative at point x,y=f(u) is derivable at the corresponding point u, then y=f[ω(x)] is derivable at the point x, and:
conforms to the chain rule of function derivation
Common compound functions Derivative of
common function derivation
piecewise function derivation
piecewise function derivation
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